Examples
Problem:
Suppose you invest $10,000 today in an account that pays 5% interest, compounded annually, how much will you have in the account at the end of 6 years?
Solution: $13,401
Next to ... |
Strike ... |
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2nd | FINANCE | ||
ENTER | |||
N= | 6 | ||
↓ | |||
I%= | 5 | the interest rate is specified as a whole number | |
↓ | |||
PV= | (-)10000 | ||
↓ | |||
PMT= | 0 | ||
↓ | |||
FV | ALPHA | SOLVE | this displays the FV next to “FV” |
Notes:
Problem:
Suppose you are promised annual payments of $1,500 each year for the next five years, with the first cash flow occurring in one year. If the interest rate is 4%, what is this stream of cash flows worth today?
Solution: $6,678
Next to ... | Strike ... |
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2nd | FINANCE | |||
ENTER | ||||
↓ | ||||
N= | 5 | |||
↓ | ||||
I%= | 4 | The interest rate is specified as a whole number | ||
↓ | ||||
↓ | ||||
PMT= | 1500 | |||
↑ | ||||
PV= | ALPHA | SOLVE | This displays the PV next to “PV=” |
Notes:
Problem:
Calculate the value of a bond with a maturity value of $1,000, a 5% coupon (paid semi-annually), five years remaining to maturity, and is priced to yield 8%.
Solution: $878.34
Note:
FV = 1,000 (lump-sum at maturity)
CF = $25 (one half of 5% of $1,000)
N = 10 (10 six-month periods remaining)
i = 4% (six-month basis, 8%/2)
Next to ... | Strike ... | ||
2nd | FINANCE | ||
↓ | |||
1:TVM Solver… | ENTER | ||
N= | 10 | ||
↓ | |||
I%= | 4 | The interest rate is specified as a whole number | |
↓ | |||
↓ | |||
PMT= | 25 | Use the arrows to go to “PMT=” | |
↓ | |||
FV= | 1000 | ||
↑ | |||
↑ | Use the arrows to go to “PV=” | ||
PV= | ALPHA | SOLVE | This results in the PV displayed as a negative number |
Notes:
Problem:
Consider the following cash flows, CF_{0} = -$10,000Solution:
Next to ... | Strike ... | ||
2nd | { | This begins the list | |
5000 | , | This is the first entry in the list | |
0 | , | This is the second entry in the list | |
2000 | , | This is the third entry in the list | |
5000 | , | This is the fourth entry in the list | |
} | This ends the list | ||
STOè | This stores the list | ||
2nd | L1 | This names the list “L1” | |
ENTER | This results in a display of the items in the list | ||
2nd | FINANCE | ||
↓ | Repeat for a total of seven times until you reach irr( | ||
7:irr( | ENTER | ||
(-)10000 | This inputs the first entry, cash flow at time 0 (the present) | ||
, | |||
2nd | L1 | Uses the same list (L1) as used for IRR | |
) | |||
ALPHA | SOLVE | This results in the IRR displayed on the screen | |
2nd | FINANCE | ||
↓ | Repeat for a total of six times until you reach npv( | ||
8:npv( | ENTER | ||
5 | , | This inputs the first entry in the NPV function, which is the interest rate specified as a whole number (that is, 5% is input as 5). | |
(-)10000 | , | This inputs the second entry in the NPV function | |
2nd | L1 | This inputs the third entry in the NPV function | |
) | |||
ALPHA | SOLVE | This results in the NPV displayed on the screen |
Note: once you enter the list and store it, you can use it for both the NPV and the IRR calculations.
Problem:
Calculate the yield to maturity of a bond with a maturity value of $1,000, a 5% coupon (paid semi-annually), ten years remaining to maturity, and is priced $857.Solution: 7.01%
Note: FV = $1,000 (lump-sum at maturity)Next to ... | Strike ... | |||
2nd | FINANCE | |||
ENTER | ||||
N= | 20 | |||
↓ | ||||
↓ | ||||
PV= | (-)857 | |||
↓ | ||||
PMT= | 25 | |||
↓ | ||||
FV= | 1000 | |||
↑ | ||||
↑ | ||||
↑ | ||||
I%= | ALPHA | SOLVE | This produces the semi-annual rate;take this value and multiply it by 2 |